So it is commonly said that what distinguishes the qualities of different vowels in a language are the frequencies of the first two or three peaks (formants) on a spectogram, so that one can plot all vowels in a two- or three-dimensional space with very little loss of information.
But I'm a little surprised by this. Even if we barely perceive formants above F5 or so, why is it not the case that the relative intensities of different formants are perceptually important as well? E.g. instead of classifying vowels like "F1 is around 720 Hz, F2 is around 1800 Hz," one could imagine classifying vowels like "F1 is about 720, F2 is around 1800 Hz and has 60% of the intensity of F1, F3 is around 2500 Hz with 20% of the intensity of F1"?
I understand that as an empirical question, just writing down F1-F3 values is good enough to distinguish vowels in all (?) known languages, so I guess I'm looking for some perceptual or physiological reason why we don't need to do some kind of more complicated Fourier analysis that takes their relative intensities into account.